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He was born at Warleywood, near Halifax, in Yorkshire, England. After studying Latin and Greek at a local grammar school, he entered St John's College, Cambridge, in 1577, and graduated in 1581.[4] In 1588, he was elected of Fellow of St. John's. In 1592 he was made reader of the physical lecture founded by Thomas Linacre; he would also read some of the mathematical lectures as well. During this period, he took an interest in navigation and astronomy, collaborating with Edward Wright.

In 1596, he became first professor in the recently founded puritan Gresham College, London; a puritan school where he taught geometry, astronomy and navigation. He would lecture there for nearly 23 years, and would make Gresham college a center of English mathematics, from which he would notably support the new ideas of Johannes Kepler.

At this time, Briggs obtained a copy of Mirifici Logarithmorum Canonis Descriptio, in which Napier introduced the idea of logarithms. Napier's formulation was awkward to work with, but the book fired Briggs' imagination - in his lectures at Gresham College he proposed the idea of base 10 logarithms in which the logarithm of 10 would be 1; and soon afterwards he wrote to the inventor on the subject. Briggs was active in many areas, and his advice in astronomy, surveying, navigation, and other activities like mining was frequently sought. Briggs in 1619 invested in the London Company, and he had two sons: Henry, who later emigrated to Virginia, and Thomas, who remained in England.[6] The lunar crater Briggs is named in his honour.

In 1616 Briggs visited Napier at Edinburgh in order to discuss the suggested change to Napier's logarithms. The following year he again visited for a similar purpose. During these conferences the alteration proposed by Briggs was agreed upon; and on his return from his second visit to Edinburgh, in 1617, he published the first chiliad of his logarithms.

In 1619 he was appointed Savilian professor of geometry at Oxford, and resigned his professorship of Gresham College in July 1620. Soon after his settlement at Oxford he was incorporated master of arts.

He also completed a table of logarithmic sines and tangents for the hundredth part of every degree to fourteen decimal places, with a table of natural sines to fifteen places, and the tangents and secants for the same to ten places; all of which were printed at Gouda in 1631 and published in 1633 under the title of Trigonometria Britannica; this work was probably a successor to his 1617 Logarithmorum Chilias Prima ("The First Thousand Logarithms"), which gave a brief account of logarithms and a long table of the first 1000 integers calculated to the 14th decimal place.

Briggs discovered, in a somewhat concealed form and without proof, the binomial theorem. English translations of Briggs's Arithmetica and the first part of his Trigonometria Britannica are available on the web.[9]

Briggs was buried in the chapel of Merton College, Oxford. Dr Smith, in his Lives of the Gresham Professors, characterizes him as a man of great probity, a condemner of riches, and contented with his own station, preferring a studious retirement to all the splendid circumstances of life.

^Cedric Clive Brown (1993), "Patronage, Politics, and Literary Traditions in England, 1558-1658", Wayne State University Press. p. 153: "Henry Briggs, the professor of mathematics, was a close friend of William Crashaw, and a committed Puritan venturer in the Virginia Company.

^Reijer Hooykaas (1974). "Scientific progress and religious dissent", Open University Press. p. 19: Like most Londoners, the founders and supervisors, as well as most of the professors, were in favour of Puritanism which in those days was the parallel 'modern' movement in politics and religion. The first professor of gemoetry (from 1599 to 1620) was Henry Briggs. Briggs numbered among his friends practically all the scientists of the day: Edward Wright, William Oughtred, Mark Ridley, and Lord Napier, to name but a few. Theologically, he was strongly puritan, having close relations with James Ussher...

^Keith Thomas (2003). "Religion and the Decline of Magic". Penguin UK. "Henry Briggs, who had abandoned the study of astrology, partly because he found no certainty in its rules, but also because he feared that 'to those who addicted themselves to the practice of divining astrology, the Devil did at first secretly lend his assistance, and at length gradatim (unless God graciously prevented) entince them into contract."